I am reading web articles on the "gh" digraph but none so far that answers my interrogation: how is is pronounced in proper names such as Callaghan, Maugham, Vaughan, McLaughlin?... Thank you for your help.
One problem here is that proper names can be pronounced pretty much however the bearer of the name wants, so the general rules don't always work with them. In your examples Maugham, Vaughan and McLaughlin do fit the general rules -- more or less. Callaghan does not.
These <gh>'s almost certainly descend from earlier spellings of velar fricative sounds, pronounced well back in the mouth, similar to the Scottish pronunciation of <ch> in loch or the German pronunciation in Bach. Over time those sounds dropped out of Early English, but their spellings stayed on with different values. In some words the <gh> fell silent before long vowel sounds, as in sigh and sleigh -- and Maugham and Vaughan. In some words, after <au> spelling short <a>, the <gh> spells [f], as in laugh, draught -- and McLaughlin with a different vowel sound.
Callaghan is the holdout, though the [h] sound is pronounced way back in the mouth the way the original velar fricative was. I once worked with a woman named Callaghan, and I suggested to her more than once that that was an odd way to spell that name, but she refused to change it to plain old <h>.
For more on the fate of <gh>, click on View all answers, then Control-F and search for <gh>.